A possible imprint of light-speed anisotropy on the CMB ICNFP2016, Crete, July 11 2016 Georgy I. Burde Alexandre Yersin Department of Solar Energy and Environmental Physics Swiss Institute for Dryland Environmental and Energy Research Jacob Blaustein Institutes for Desert Research, Ben-Gurion University Sede-Boker Campus, 84990, Israel Moscow, July 5, 2007 Outline Moscow, July 5, 2007 The modern view is that there exists a preferred frame of reference related to the cosmic microwave background (CMB), more precisely to the last scattering surface (LSS), and that our galaxy's peculiar motion with respect to the CMB produces Doppler effect responsible for the CMB temperature anisotropies. It is evident that the existence of a preferred frame of reference is in contradiction with the fundamental hypothesis of the special relativity which Einstein termed the 'principle of relativity'. A violation of the relativity principle influences also a validity of the principle of universality of the speed of light, in particular its constancy and isotropy, and, in general, implies a violation of the special relativity. Nevertheless, the special relativity formulas are commonly used in the context of cosmology when there is a need to relate physical effects in the frames moving with respect to each other. Moscow, July 5, 2007 Example: the CMB temperature anisotropy due to our galaxy's peculiar motion The CMB temperature angular distribution due to the Doppler effect is a pure dipole pattern in terms of the angle between the line of sight and the direction of the observer motion, measured in the frame of the source. Due to the effect of light aberration this angle transforms into the angle measured in the moving frame of the observer and, as the result, the quadrupole and higher moments arise β2 T (θ~) = T 1 + +β cos θ~ + cos 2θ~ 0 2 Derivation of this formula is based on the Lorentz transformations of the relativity theory. Moscow, July 5, 2007 Lorentz transformations X − vT T − vX =c2 x = ; y = Y ; z = Z; t = p1 − v 2=c2 p1 − v 2=c2 Moscow, July 5, 2007 Doppler effect A source of electromagnetic radiation (light) is in a reference frame S and the observer is in the frame S0 moving with velocity v with respect to S 1 − β cos Θ νr = νe p1 − β2 where Θ is the angle between the wave vector and the direction of motion, measured in the frame of the source S. The aberration formula β − cos θ~ cos Θ = 1 − β cos θ~ where θ~ is the angle between the line of sight and the direction of the observer motion, measured in the frame of the observer. The frequency shift relation 1 1 − β2 2 νr = νe 1 − β cos θ~ Moscow, July 5, 2007 In the context of the CMB anisotropy T (θ~) T = 0 νr νe where T0 is the effective temperature measured by the observer, that is at rest relative to the LSS and sees strictly isotropic blackbody radiation and T (θ~) is the effective temperature of the blackbody radiation for the moving observer looking in the fixed direction θ~. Using the relation for the frequency shift yields 1 1 − β2 2 T (θ~) = T0 1 − β cos θ~ β2 T (θ~) = T 1 + +β cos θ~ + cos 2θ~ 0 2 Moscow, July 5, 2007 'Test theories' The discovery of the cosmic background radiation, which has shown that cosmologically a preferred system of reference does exist, and the fact, that some of modern theories suggest a violation of special relativity, resulted in renewed interest in sensitive experimental tests of relativity. To describe tests of basic principles underlying a theory and to quantitatively express the degree of agreement between experiments and these principles, a theory which allows violations of these principles is required. The Mansouri and Sexl test theory framework It is assumed that there exists a preferred inertial reference frame ("ether frame"), in which the speed of light is isotropic. Generalized transformations between a preferred frame and a moving frame are postulated. Since the only preferred frame one may think of is the cosmological frame, in which the microwave background radiation is isotropic, the preferred frame of reference is identified with the CMB frame. Moscow, July 5, 2007 Transformations postulated in the Mansouri and Sexl (MS) test theory t = a(v)T + 1(v)x + 2(v)y + 3(v)z x = d(v)X + (b (v) − d (v)) − b(v)vT y = d(v)Y ; z = d(v)Z Abolition of the relativity principle Anisotropy of the two-way speed of light in the frame moving with respect to the preferred frame. Moscow, July 5, 2007 Conventionality of simultaneity and anisotropic propagation of light Simultaneity at distant space points of an inertial system is defined by a clock synchronization that makes use of light signals. We have empirical access only to the round-trip (two-way) average speed of light. There exists inescapable entanglement between remote clock synchronization and one-way velocity of light. If a light ray is emitted from the master clock and reflected off the remote clock one has a freedom to give the reflection time t at the remote clock any intermediate time in the interval between the emission and reception times Moscow, July 5, 2007 t + t 1 Einstein (standard) synchronization : t(s) = 0 A = t + (t − t ) R 2 0 2 A 0 1 Non − standard synchronization : t = t + (t − t ); 6= R 0 A 0 2 1 + k c c = ; V+ = : V− = 2 1 + k 1 − k Moscow, July 5, 2007 If the described procedure is used for setting up throughout the frame of a set of clocks using signals from some master clock placed at the spatial origin x x t0 + tA 1 1 tR = t0 + ; tA = tR + ; ) tR = + x − V+ V− 2 2V+ 2V− t + t k x k x t = 0 A + = t(s) + R 2 c R c Moscow, July 5, 2007 Thus, a difference in the standard and nonstandard clock synchronization may be reduced to a change of coordinates k x t = t(s) + ; x = x(s) (1) c where t(s) is the time setting according to Einstein (standard) synchronization procedure. Moscow, July 5, 2007 Round-trip postulate cn c V (n) = or V (Θ) = 1 + kn 1 + k cos Θ k r t = t(s) + ; r = r(s) c Moscow, July 5, 2007 Generalized Lorentz transformations (Edwards (1963), Winnie (1970), Ungar (1986) and others) 2 X − cT β cT (1 − 2kβ) − X 1 − k β v x = q ; ct = q ; β = 2 2 2 2 c (1 − kβ) − β (1 − kβ) − β Applying the transformation from the non-standard synchronization to the standard one k x k X t = t(s) + ; x = x(s); T = T (s) + ; X = X (s) c c yields the Lorentz transformations (s) (s) X − cT βs (s) cT − X βs vs x = ; ct = ; βs = p 2 p 2 1 − βs 1 − βs c It could be expected since the derivation is based on the assumption that, in the case of k = 0 (standard synchronization), the relations of the special relativity theory are valid. Moscow, July 5, 2007 From the statement that There exists inescapable entanglement between remote clock synchronization and one-way speed of light the conclusion is made that The one-way speed of light is irreducibly conventional in nature. It is not correct The one-way velocity cannot be defined separately from the synchronization choice but there could be measurable effects which allow to distinguish a specific value of the one-way speed of light and the corresponding synchronization from others. Moscow, July 5, 2007 The 'Generalized Lorentz Transformations' (GLT), commonly considered as showing conventionality of the one-way speed of light, prove the opposite. The GLT are conceptually inconsistent: the one-way speed of light is assumed to be anisotropic but the relations of the standard special relativity based on isotropy of the one-way speed of light are used. Thus, the GLT are the Lorentz transformations distorted by a change of variables and all predictions (measurable effects) based on the GLT are the same as in the special relativity theory. The inconsistency is illustrated by that the GLT does not satisfy the Correspondence principle: in the limit of small velocities, the formula for transformation of the coordinate x turns into that of the Galilean transformation x = X − vT = X − βcT For the GLT: X − cT β v x = q ) x = X − βcT + kβX as β = ) 0 2 2 c (1 − kβ) − β Moscow, July 5, 2007 The correspondence principle selects the isotropic one-way speed of light and the corresponding Einstein synchronization from all others Thus, both the Lorentz transformations and the GLT describe the situation when there is no anisotropy in a physical system and correspondingly no anisotropy of the one-way speed of light. All predictions (measurable effects) of such a theory are valid only for the isotropic situation. The Generalized Lorentz transformations cannot provide a basis for kinematics of the special relativity if an anisotropy of the one-way speed of light is due to a real space anisotropy The special relativity kinematics applicable to that situation should be developed based on the first principles, without refereeing to the relations of the standard relativity theory. Moscow, July 5, 2007 The basis of the special relativity Principle of relativity, which states the equivalence of all inertial frames as regards the formulation of the laws of nature Universality of light propagation in inertial frames The two principles imply Invariance of the equation of light propagation with respect to the coordinate transformations between inertial frames.